This is a 12x12 Killer-X. Not sure what the correct term is for the 12-cell equivalent of a nonet, so I’ll just call it a Box, numbering B1 to B12. For simplicity I’m calling the candidates 1-9, then A=10, B=11 and C=12, rather than 1-12, since it makes diagrams easier.

For a 12x12 killer, the 45 rule becomes the 78 rule.

I’ll skip Prelims; even for 2-cell cages, most won’t eliminate many candidates.

1. 78 rule on B1 1 innie R3C1 = 7

2. 78 rule on B12 1 innie R10C12 = 7

3. 78 rule on B2+B3 1 outie R4C8 = 3, R3C8 = 8

4. 78 rule on B10+B11 1 outie R9C5 = 7, R10C5 = 3

4a. 9(2) cage at R1C5 = {45} (only remaining combination), locked for C5 and B2

5. 21(2) cage at R1C8 = {9C/AB}

5a. 21(2) cage at R1C10 = {9C/AB}

5b. Naked quad {9ABC} in 21(2) cages, locked for R1

6. 13(2) cage at R1C6 = {67} (only remaining combination), locked for R1 and B2

7. 78 rule on R1 3 innies R1C1 + R1C5 + R1C12 = 9 = {135/234}, 3 locked for R1

7a. R1C5 = {45} -> R1C1 + R1C12 = {13/23}

7b. 14(3) cage at R1C2 = {158/248}, 8 locked for B1

8. 78 rule on B3 2 outies R1C8 + R2C8 = 19 = {9A} (only remaining combination), locked for C8 and B2, clean-up: no 9,A in R1C9

8a. B,C in R1 only in R1C9 + R1C10 + R1C11, locked for B3

9. 12(2) cage at R3C5 = {1B} (only remaining combination), locked for R3 and B2

10. 20(2) cage at R5C7 = [8C/9B] -> R5C7 = {89}, R5C8 = {BC}

11. 78 rule on B10 2 outies R11C5 + R12C5 = 20 = {8C/9B}

11a. 15(2) cage at R12C4 = [3C/4B/69/78], R12C3 = {3467}

11b. Min R11C5 = 8 -> max R11C34 = 7, R11C34 = {123456}

12. 18(2) cage at R8C4 = {6C/7B/8A}, no B in R8C4

13. 78 rule on B7 2 innies R7C34 = 19 = {7C/8B/9A}

13a. 16(2) cage at R6C3 = [4C/5B/6A/79/97], no 8 in R7C3, no B in R7C4

14. 78 rule on B4 2 remaining innies R4C4 + R6C3 = 16 = [79/97/A6/B5/C4]

14a. 17(2) cage at R4C4 = [7A/98/B6], clean-up: no 4,6 in R6C3, no A,C in R7C3, no 7,9 in R7C4 (step 13)

15. 78 rule on B8 1 outie R7C4 = 1 remaining innie R9C8 + 7 -> R7C4 = {8C}, R9C8 = {15}, clean-up: no 9 in R7C3 (step 13), no 7 in R6C4, no 9 in R4C4 (step 14), no 8 in R4C5

15a. 11(2) cage at R9C8 = [1A/56]

15b. 18(2) cage at R8C4 (step 12) = {6C/8A} (cannot be {7B} which clashes with R7C3), no 7,B

15c. Killer pair 8,C in R7C4 and 18(2) cage, locked for C4 and B7

16. 6(2) cage at R7C8 = {24} (only remaining combination, cannot be {15} which clashes with R9C8), locked for C8 and B8

17. 21(2) cage at R7C7 = {9C/AB }

18. 13(2) cage at R11C8 = {1C/67}

19. 14(2) cage at R10C7 = [2C/86/95]

20. 13(2) cage at R9C6 = {1C/3A/58}

21. 13(2) cage at R9C6 (step 20) = {1C/3A/58}, 11(2) cage at R9C8 (step 15a) = [1A/56] -> combined cage R9C6789 = {1C}[56]/{3A}/[56]/{58}[1A], 5 locked for R9 and B8

22. 15(2) cage at R8C5 = [69/96/C3]

22a. 21(2) cage at R7C7 (step 17) = {AB} (only remaining combination, cannot be 9C which clashes with 15(2) cage), locked for C7 and B8

23. 13(2) cage at R9C6 (step 20) = {1C/58}, no 3

23a. Killer pair 1,5 in 13(2) cage and R9C8, locked for R9 and B8

24. 23(3) cage at R7C4 = [869/896/8C3/C83], R7C6 = {369}, 8 locked for R7

24a. 3 in B8 only in R78C6, locked for C6

25. 14(2) cage at R5C5 = {2C/68}

26. R4C5 = A (hidden single in C5), R4C4 = 7, placed for D\, R6C3 = 9 (step 14), R7C3 = 7, R7C4 = C (step 13)

26a. 18(2) cage at R8C4 (step 15b) = {8A} (only remaining combination), locked for C4 and B7

27. 23(3) cage at R7C4 (step 24) = [C83] (only remaining permutation) -> R7C5 = 8, R7C6 = 3, placed for D/

28. R1C1 = 3 (hidden single in R1), placed for D\

29. 14(2) cage at R5C5 (step 25) = {2C} (only remaining combination), locked for C5 and B5 -> R5C8 = B, placed for D/, R5C7 = 9, clean-up: no 5 in R10C8

29a. Naked pair {9B} in R11C5 + R12C5, locked for C5 and B11 -> R3C5 = 1, R3C6 = B, R8C5 = 6, placed for D/, R8C6 = 9

30. 10(2) cage at R4C6 = {46} (only remaining combination), locked for R4 and B5

31. 9(2) cage at R5C6 = {18} (only remaining combination), locked for C6 and B5

32. Naked pair {57} in R6C78, locked for R6, R6C9 = A (cage total), R9C9 = 6, placed for D\, R9C8 = 5, R6C8 = 7, R6C7 = 5, placed for D/, R9C6 = C, R9C7 = 1, R2C6 = 2

33. 13(2) cage at R11C8 (step 18) = {1C} (only remaining combination), locked for B11 -> R10C8 = 6, R10C7 = 8

34. 8(2) cage at R7C9 = [17/53]

34a. 8(2) cage at R7C11 = [17/53]

34b. Naked pair {15} in R7C9 + R7C11, locked for R7 and B9

34c. Naked pair {37} in R8C9 + R8C11, locked for R8 and B9

35. 78 rule on B9+B12 1 outie R6C10 = 6, R7C10 = B, R78C7 = [AB]

36. 24(3) cage at R8C10 = {2AC/48A}, no 9, A locked for B9

36a. 9 in B9 only in R79C12, locked for C12

37. 15(2) cage at R12C4 = [4B/69], no 3

37a. R56C4 = [24/42/51]

38. R11C4 = 3 (hidden single in C4)

38a. 78 rule on B10 2 remaining innies R11C3 + R12C4 = 7 -> R11C3 = 1, R12C4 = 6, R12C5 = 9, R11C5 = B, R11C8 = C, R12C8 = 1

38. 78 rule on R12 2 innies R12C1 + R12C12 = 13 = [2B/85]

38a. 9(2) cage at R12C6 = [54/72]

38b. Killer pair 2,5 in R12C1 + R12C12 and 9(2) cage, locked for R12

39. 3 in R12 only in 25(3) cage at R12C9 = {3AC} (only remaining combination), locked for R12 and B12

40. A in C12 only in 14(3) cage at R1C12 = {13A} (only remaining combination) -> R1C12 = 1, placed for D/, R23C12 = {3A}, locked for C12 and B3

41. 21(2) cage at R1C10 = {9C} (only remaining combination), locked for R1 and B3 -> R1C89 = [AB]

42. R2C8 = 9 -> 22(3) cage at R2C8 = {589} (only remaining combination), locked for R2, 5,8 also locked for B3 -> R2C5 = 4, R1C5 = 5

43. Naked pair {24} in R3C9 + R3C10, locked for R3 and B3 -> R2C11 = 7, placed for D/, R3C11 = 6, R8C11 = 3, R7C11 = 5, R78C9 = [17]

44. 6(2) cage at R5C4 = [51] (cannot be {24} which clashes with R1C4), R6C6 = 8, placed for D\, R5C6 = 1

45. R23C4 = [B9] = 20 -> R23C3 = 11 = {56} -> R2C3 = 6, R3C3 = 5, placed for D\, R12C12 = B, R12C1 = 2 (step 38), placed for D/, R3C10 = 4, placed for D/, R3C9 = 2, R12C7 = 4, R12C6 = 5, R4C67 = [46], R1C67 = [67], R10C6 = A, R11C67 = [72], R12C23 = [78]

46. R10C4 = 4, R10C3 = C, placed for D/

46a. R10C34 = [C4] = 16 -> R10C2 + R11C2 = 19 = {9A} -> R10C2 = 9, R11C2 = A, placed for D/, R9C4 = 8, placed for D/, R8C4 = A, R4C9 = 9, R5C9 = 3

47. 14(3) cage at R1C2 = [842], R8C3 = 2, R8C8 = 4, placed for D\, R7C8 = 2, R11C11 = 9, R3C2 = C, R2C2 = 1, placed for D\, R2C1 = A, R10C9 = 5, R10C10 = 2, placed for D\, R5C5 = C, R6C5 = 2

48. 9(2) cage at R5C2 = {36} (only remaining combination) -> R5C2 = 6, R6C2 = 3

49. R23C7 = [C3], R2C9 = 8, R2C10 = 5, R23C12 = [3A], R7C2 = 4, R7C12 = 9, R7C1 = 6, R8C1 = 1, R8C2 = 5, R10C1 = B, R11C1 = 5, R10C11 = 1, R11C9 = 4, R11C10 = 8, R11C12 = 6, R8C10 = C, R1C10 = 9, R1C11 = C, R45C10 = [17], R9C10 = A, R9C11 = 2 (cage sum), R8C12 = 8, R9C12 = 4, R12C9 = C, R12C10 = 3, R12C11 = A, R5C12 = 2, R4C23 = [2B], R4C11 = 8, R4C1 = C, R4C12 = 5, R56C1 = [84], R5C3 = A, R56C11 = [4B], R6C12 = C, R9C123 = [9B3]